A348067 Matula-Goebel tree number of tree n with a new leaf added below each existing vertex.

2, 6, 26, 18, 202, 78, 122, 54, 338, 606, 2462, 234, 794, 366, 2626, 162, 1346, 1014, 502, 1818, 1586, 7386, 4546, 702, 20402, 2382, 4394, 1098, 8914, 7878, 43954, 486, 32006, 4038, 12322, 3042, 2962, 1506, 10322, 5454, 12178, 4758, 4946, 22158, 34138, 13638

Offset

1,1

Comments

k times nested a(a(...a(1))) = A076146(k+1) is the Matula-Goebel number of the binomial tree order k constructed by an "expansion" method starting from a singleton and successively adding a new leaf under every vertex.

Links

Kevin Ryde, Table of n, a(n) for n = 1..5000

Index entries for sequences related to Matula-Goebel numbers

Formula

a(n) = 2 * Product_{i=1..k} prime(a(primepi(p[i]))), where n = p[1]*...*p[k] is the prime factorization of n with multiplicity (A027746).

Example

tree n=6   tree a(6) = 78
  R             R___        root R
  | \           |\  \
  A  B          A @  B      new vertices
  |             |\    \     "@" below each
  C             C @    @    existing
                 \
                  @

Prog

(PARI) a(n) = my(f=factor(n)); 2*factorback([prime(self()(primepi(p))) | p<-f[, 1]], f[, 2]);

Crossrefs

Cf. A027746 (prime factors), A076146 (binomial tree).

Cf. A297002 (add leaves under children of the root).

Sequence in context: A178087 A109286 A009466 * A032479 A029988 A050573

Adjacent sequences: A348064 A348065 A348066 * A348068 A348069 A348070

Keyword

nonn

Author

Kevin Ryde, Oct 01 2021

Status

approved